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Math Help - inversed Z Transform

  1. #1
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    inversed Z Transform

    Hello!
    I have a question,could you please give an idea about how can I calculate an inversed Z transform of these ( Z^(-1)[...] ) :

    z/(z^2+z+1)

    and

    z^2/(z^2+z+1)

    Thank you in advance.
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  2. #2
    Senior Member bkarpuz's Avatar
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    Quote Originally Posted by inzaghina View Post
    Hello!
    I have a question,could you please give an idea about how can I calculate an inversed Z transform of these ( Z^(-1)[...] ) :

    z/(z^2+z+1)

    and

    z^2/(z^2+z+1)

    Thank you in advance.
    You should probably factorize.
    Also you may refer to Mathematica 7.0 - InverseZTransform.
    As a little note, if \lim\nolimits_{z\to\infty}F(z)/z\neq0, then we can not find an exponentially bounded sequence \{f(n)\} for which [tex]f(n)=Z^{-1}\{F(z)\}(n)[\math] holds.
    Last edited by bkarpuz; November 1st 2009 at 01:09 PM.
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  3. #3
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    Well, I have to do that by hand, not in the computer.
    And I did a mistake, I have to solve Z^(-1) of :

    z/(z^2+z+1)^2

    and

    z^2/(z^2+z+1)^2

    have a good day!
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by inzaghina View Post
    Hello!
    I have a question,could you please give an idea about how can I calculate an inversed Z transform of these ( Z^(-1)[...] ) :

    z/(z^2+z+1)
    divide top and bottom by z^2 to get:

    \frac{z^{-1}}{z^{-2}+z^{-1}+1}

    then look this up in a table of inverse z-transforms (item 18 in the table in the Wikipedia article on the z-transform looks like what you need)

    CB
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